渐近非局部平均图像去噪算法

邢笑笑; 王海龙; 李健; 张选德

doi:10.16383/j.aas.c190294

渐近非局部平均图像去噪算法

doi: 10.16383/j.aas.c190294

1.
陕西科技大学电子信息与人工与智能学院西安 710021
2.
宁夏师范学院数学与计算机科学学院固原 756000

基金项目: 国家自然科学基金(61871260, 61362029, 61811530325, 61871259, 61603234)资助

详细信息

作者简介:
邢笑笑：陕西科技大学电子信息与人工智能学院硕士研究生. 2017年获得吉林农业大学工学学士学位. 主要研究方向为图像处理, 图像去噪. E-mail: xingxiao_0918@163.com

王海龙：宁夏师范学院数学与计算机科学学院讲师. 2011年获得香港公开大学教育硕士学位. 主要研究方向为代数. E-mail: wanghailong7903@163.com

李健：陕西科技大学电子信息与人工智能学院教授. 2002年获得浙江大学工学博士学位. 主要研究方向为图形图像处理, 大数据挖掘与机器学习, 网络与信息安全. E-mail: lijianjsj@sust.edu.cn

张选德：陕西科技大学电子信息与人工智能学院教授. 2013年获得西安电子科技大学理学博士学位. 主要研究方向为图像恢复, 图像质量评价, 稀疏表示和低秩逼近理论. 本文通信作者. E-mail: zhangxuande@sust.edu.cn

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出版历程
- 收稿日期: 2019-04-11
- 录用日期: 2019-09-09
- 网络出版日期: 2020-09-28
- 刊出日期: 2020-09-28

Asymptotic Non-local Means Image Denoising Algorithm

1.
School of Electronic Information and Artificial Intelligence, Shaanxi University of Science and Technology, Xi'an 710021
2.
School of Mathematics and Computer Science, Ningxia Normal University, Guyuan 756000

Funds: Supported by National Natural Science Foundation of China (61871260, 61362029, 61811530325, 61871259, 61603234)

摘要

摘要: 非局部平均去噪算法(Non-local means denoising algorithm, NLM)是图像处理领域具有里程碑意义的算法, NLM的提出开启了影响深远的非局部方法. 本文从以下两个方面来重新探讨非局部平均算法: 1) 针对NLM算法运算复杂度高的问题, 基于互相关(Cross-correlation, CC)和快速傅里叶变换(Fast Fourier transformation, FFT)构造了一种快速算法; 2) NLM在滤除噪声的同时会模糊图像结构信息, 在强噪声条件下更是如此. 针对这一问题, 提出了一种渐近非局部平均图像去噪算法, 该算法利用方差的性质来控制滤波参数. 数值实验表明, 快速算法较之经典算法, 在标准参数配置下运行速度可提高27倍左右; 渐近非局部平均图像去噪算法较之经典非局部平均图像去噪算法, 去噪效果显著改善.
- 图像去噪 /
- 非局部平均 /
- 快速算法 /
- 渐近非局部平均
Abstract: Non-local means denoising (NLM) algorithm is a milestone algorithm in the field of image processing. The proposal of NLM has opened up the non-local method which has a deep influence. This paper performed a revisit for NLM from two aspects as follows: 1) To alleviate the high computational complexity problem of NLM, a fast algorithm was constructed, which was based on cross-correlation and fast Fourier transform; 2) NLM always blur structures and textures during the noise removal, especially in the case of strong noise. To solve this problem, an asymptotic non-local means (ANLM) image denoising algorithm is put forward, which uses the property of noise variance to control the filtering parameters. Numerical experiments illustrate that the fast algorithm is 27 times faster than classical implementation with standard parameter configuration, and the ANLM obtain better denoising effect than classical NLM.
- Image denoising /
- non-local means (NLM) /
- fast algorithm /
- asymptotic non-local means (ANLM)

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图 1 像素点i处的取块示意图

Fig. 1 The schematic of taking blocks at pixel points i

下载: 全尺寸图片幻灯片

图 2 滤波参数的大小对权值的影响

Fig. 2 The influence of filter parameter size on the weight

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图 3 NLM滤波与原图的效果比较

Fig. 3 Effect comparison of NLM and original image

下载: 全尺寸图片幻灯片

图 4 渐近非局部的滤波结果

Fig. 4 Denoising result of asymptotic non-local

下载: 全尺寸图片幻灯片

图 5 三种算法对噪声图像的效果比较

Fig. 5 Effect comparison of three algorithms on noisy image

下载: 全尺寸图片幻灯片

图 6 三种算法对局部噪声图像的效果比较

Fig. 6 Effect comparison of three algorithms on local noisy image

下载: 全尺寸图片幻灯片

表 1 三种去噪算法运行速度的比较

Table 1 Comparison of running speeds of three denoising algorithms

图像块尺寸	搜索区域尺寸	NLM运行时间 (s)	NLM-P运行时间 (s)	FNLM运行时间 (s)	NLM与NLM-P 运行时间之比值	NLM与FNLM 运行时间之比值	NLM-P与FNLM 运行时间之比值
3 × 3	21 × 21	232.79	19.41	7.17	11.99	32.46	2.71
3 × 3	31 × 31	505.64	42.01	10.53	12.04	48.02	3.99
3 × 3	51 × 51	873.02	113.04	13.95	7.72	62.58	8.10
3 × 3	101 × 101	5 024.73	160.10	48.49	31.38	103.62	3.30
5 × 5	21 × 21	236.12	18.29	8.68	12.91	27.20	2.11
5 × 5	31 × 31	512.77	39.90	12.74	12.85	40.25	3.13
5 × 5	51 × 51	911.16	108.04	16.19	8.43	56.28	6.67
5 × 5	101 × 101	5 159.80	154.83	53.13	33.33	97.12	2.91
7 × 7	21 × 21	250.77	19.21	11.28	13.05	22.23	1.70
7 × 7	31 × 31	547.50	42.29	16.51	12.95	33.16	2.56
7 × 7	51 × 151	913.15	114.37	19.75	5.58	46.24	5.79
7 × 7	101 × 101	5 328.55	163.56	59.96	32.58	88.87	2.73
9 × 9	21 × 21	256.49	18.54	13.40	13.83	19.14	1.38
9 × 9	31 × 31	560.17	39.63	20.70	14.13	27.06	1.91
9 × 9	51 × 51	969.08	108.74	23.35	8.91	41.50	4.66
9 × 9	101 × 101	5 516.60	154.75	67.41	35.65	81.84	2.30

下载: 导出CSV

表 2 三种去噪算法对灰度图像的效果比较

Table 2 Effect comparison of three denoising algorithms on gray images

图像	算法	25	30	50	75	100
图像	算法	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM
Camera 256 × 256	NLM	28.23/0.77	27.27/0.73	24.26/0.57	21.82/0.41	20.17/0.30
	PNLM	28.39/0.82	27.58/0.79	24.96/0.71	22.59/0.61	21.02/0.52
	ANLM	28.07/0.83	27.43/0.81	25.35/0.73	23.32/0.64	21.80/0.56
Lena 512 × 512	NLM	30.11/0.89	29.13/0.87	26.21/0.78	23.75/0.67	22.00/0.58
	PNLM	30.58/0.89	29.72/0.88	27.18/0.81	25.07/0.73	23.65/0.67
	ANLM	30.59/0.90	29.80/0.89	27.57/0.83	25.72/0.77	24.35/0.71
Boat 512 × 512	NLM	28.17/0.85	27.21/0.82	24.53/0.72	22.48/0.61	21.04/0.53
	PNLM	28.40/0.85	27.51/0.82	24.99/0.72	23.17/0.63	22.07/0.56
	ANLM	28.55/0.86	27.74/0.84	25.50/0.75	23.73/0.67	22.58/0.61
Finger 512 × 512	NLM	26.57/0.93	25.43/0.91	21.84/0.79	19.18/0.63	17.73/0.51
	PNLM	26.41/0.93	25.45/0.91	22.15/0.78	19.22/0.57	17.64/0.40
	ANLM	26.41/0.94	25.63/0.93	23.00/0.83	20.40/0.68	18.58/0.52
B Fly 512 × 512	NLM	28.09/0.85	27.12/0.82	23.88/0.69	20.61/0.54	18.39/0.41
	NLM	27.78/0.88	26.98/0.86	24.32/0.79	21.44/0.68	18.99/0.56
	ANLM	27.61/0.89	26.84/0.87	24.65/0.80	22.44/0.72	20.45/0.63
Man 512 × 512	NLM	28.28/0.85	27.39/0.82	24.87/0.71	22.83/0.61	21.35/0.53
	PNLM	28.45/0.84	27.62/0.81	25.32/0.71	23.61/0.62	22.51/0.56
	ANLM	28.63/0.86	27.89/0.83	25.83/0.75	24.20/0.67	23.08/0.61
Baboon 512 × 512	NLM	24.53/0.81	23.66/0.77	21.60/0.63	20.27/0.52	19.36/0.44
	PNLM	24.61/0.81	23.75/0.76	21.51/0.59	20.23/0.47	19.61/0.40
	ANLM	24.62/0.83	23.88/0.79	21.83/0.64	20.57/0.53	19.90/0.45
Straw 256 × 256	NLM	24.67/0.80	23.50/0.74	20.71/0.55	19.16/0.39	18.27/0.31
	PNLM	24.94/0.81	23.78/0.75	20.66/0.51	18.96/0.32	18.25/0.24
	ANLM	24.96/0.83	24.04/0.78	21.23/0.58	19.37/0.40	18.51/0.32
Barbara 512 × 512	NLM	28.26/0.89	27.11/0.87	24.05/0.76	21.92/0.65	20.54/0.57
	PNLM	28.76/0.90	27.64/0.88	24.51/.078	22.45/0.68	21.30/0.60
	ANLM	28.72/0.91	27.82/0.89	25.08/0.81	23.02/0.71	21.82/0.65
Montage 256 × 256	NLM	30.31/0.83	29.17/0.78	25.54/0.62	22.21/0.44	20.24/0.33
	PNLM	30.56/0.88	29.50/0.86	26.41/0.79	23.51/0.69	21.31/0.59
	ANLM	30.60/0.89	29.65/0.87	27.04/0.80	24.50/0.71	22.28/0.62
House 256 × 256	NLM	30.60/0.78	29.43/0.74	25.92/0.57	23.20/0.41	21.43/0.30
	PNLM	31.30/0.83	30.26/0.81	26.97/0.73	24.31/0.62	22.74/0.54
	ANLM	31.28/0.84	30.47/0.82	27.85/0.75	25.35/0.66	23.58/0.58
Hill 512 × 512	NLM	28.21/0.83	27.33/0.79	24.94/0.68	23.08/0.58	21.68/0.51
	PNLM	28.37/0.82	27.51/0.78	25.31/0.66	23.87/0.57	23.01/0.52
	ANLM	28.69/0.84	27.94/0.81	25.86/0.71	24.38/0.62	23.44/0.57
Couple 512 × 512	NLM	27.50/0.84	26.52/0.80	24.03/0.69	22.16/0.58	20.84/0.50
	PNLM	27.76/0.84	26.74/0.80	24.27/0.67	22.68/0.57	21.71/0.51
	ANLM	28.12/0.86	27.21/0.83	24.79/0.72	23.22/0.62	22.20/0.56
Peppers 256 × 256	NLM	28.61/0.79	27.58/0.75	24.45/0.60	21.76/0.45	20.00/0.34
	PNLM	29.04/0.83	28.08/0.80	25.12/0.72	22.40/0.62	20.64/0.53
	ANLM	28.75/0.84	27.93/0.81	25.51/0.74	23.34/0.65	21.64/0.57

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